A student sits on a rotating stool holding two 3.09-kg masses. When his arms are

Question

A student sits on a rotating stool holding two 3.09-kg masses. When his arms are extended horizontally, the masses are 1.08 m from the axis of rotation, and he rotates with an angular speed of 0.751 rad/s The moment of inertia of the student plus stool is 3.25 kg m^2 and is assumed to be constant. (Note that this moment of inertia does not include the two 3.09-kg masses.) The student then pulls the masses horizontally to 0.34 m from the rotation axis, (a) Find the new angular speed of the student. Find the kinetic energy of the rotating system (student, stool, and masses) (b) before and (c) after the masses are pulled in. Caution: There are two weights. The new angular speed of the student. rad's ( plusminus 0.02 rad's) Kinetic energy before the masses are pulled in. J ( plusminus 0.02 J) Kinetic energy after the masses are pulled in. J ( plusminus 0.02 J) Source: Serway and Faughn, College Physics, 5th edition, Problem 8.47

Explanation / Answer

initial moment of inertia, Ii = 3.25 + ( 2 x3.09 x 1.08^2)

Ii = 10.46 kg m^2

final moment of inertia, If = 3.25 + (2 x 3.09 x 0.34^2) = 3.96 kg m^2

a) using angular momemntum conservation (Iw)

10.46 x 0.751 = 3.96 x wf

wf = 1.98 rad/s

b) KEi = Iw^2 /2 = 10.46 x 0.751^2 /2 = 2.95 J

c) KEf = 3.96 x 1.98^2 /2 = 7.76 J

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